{
  "id": "1505.05168",
  "version": "v1",
  "published": "2015-05-19T20:15:48.000Z",
  "updated": "2015-05-19T20:15:48.000Z",
  "title": "Good Reduction for Endomorphisms of the Projective Line in Terms of the Branch Locus",
  "authors": [
    "J. K. Canci"
  ],
  "comment": "23 pages, comments are welcome",
  "categories": [
    "math.NT",
    "math.AG",
    "math.DS"
  ],
  "abstract": "Let $K$ be a number field and $v$ a non archimedean valuation on $K$. We say that an endomorphism $\\Phi\\colon \\mathbb{P}_1\\to \\mathbb{P}_1$ has good reduction at $v$ if there exists a model $\\Psi$ for $\\Phi$ such that $\\deg\\Psi_v$, the degree of the reduction of $\\Psi$ modulo $v$, equals $\\deg\\Psi$ and $\\Psi_v$ is separable. We prove a criterion for good reduction that is the natural generalization of a result due to Zannier in \\cite{Uz3}. Our result is in connection with other two notions of good reduction, the simple and the critically good reduction. The last part of our article is dedicated to prove a characterization of the maps whose iterates, in a certain sense, preserve the critically good reduction.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-19T20:15:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11S15",
      "37P05",
      "14G99"
    ],
    "keywords": [
      "branch locus",
      "projective line",
      "endomorphism",
      "non archimedean valuation",
      "natural generalization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150505168C"
    }
  }
}